I'm not looking forward to meeting Woody Harrelson. I'm a bit scared, to be honest. I've just seen Rampart, his new movie in which he plays a racist, psychopathic police officer. Harrelson is terrifying in it. Terrifying when he's chasing villains, bullying juniors, beating the crap out of innocents, stalking the mothers of his children. He's even terrifying when he's making love. His body, specially slimmed-down and muscled-up for the part, pulses with a tension permanently on the cusp of violence.

It's not as if this is a one-off – there's his sickening Mickey Knox in Natural Born Killers ("At birth, I was cast into a flaming pit of scum"), deranged killer Tallahassee in Zombieland, Charlie in the forthcoming Seven Psychopaths whose title says it all, and we've barely started. Even when he plays it nice, like he did in Cheers all those years ago as dopey bartender Woody, there's something in the goofy smile that makes you worry – for his sanity, and your safety. And it's not as if the weird stuff is just confined to acting – there are numerous stories of him hitting photographers or police officers or taxi doors.

It's Sunday afternoon and when I arrive at the London hotel, there's no sign of Harrelson. His publicist apologises and says the bad news is he's still in bed, but the good news is he's woken up. A few minutes later he arrives, looking a little the worse for wear. He stretches, gulps from a hefty bottle of water, and drawls a lazy Texan apology. "I tied one on last night," he says, "I drank too much." Where did he go? "We went to a few places… but I'm waking up now and everything seems nice and, erm, Victorian in this room." Harrelson takes another swig, and as he does, I'm again thinking of the crazed cop in Rampart.

Even when Harrelson plays it nice, like he did in Cheers all those years ago as dopey bartender Woody, there’s something in the goofy smile that makes you worry. Photograph: NBCUPHOTOBANK/Rex NBCUPHOTOBANK / Rex Features/NBCUPHOTOBANK/Rex

Doesn't it take a lot out of him making a film like that – after all, he's in virtually every scene, inflicting damage of one sort or another? "It was an intense time," he says. "The problem was being seeped in paranoia because that was so much the attitude of the character. That really affected me because I don't normally do paranoia." He pauses. "Well, sometimes, of course. But it's an emotion I try not to affect myself with. I had weird shit happening." What weird shit? "Not stuff I'd care to talk about. But being aggressive and strange with friends who had not been offensive, but I took it as offensive. A couple of friends said, 'I can't wait till you're done with this role because I know this ain't you doing it.' "

What messed with his head more, Rampart or Natural Born Killers? The latter film, directed by Oliver Stone, was blamed for a series of copycat killings after it was released in 1994. "I'd say this, but then when I was doing Natural Born Killers I was doing some weird shit, too." I tell him I can't bear watching it; that it freaks me out. He smiles. "Really, it's a misunderstood romantic comedy." And now his smile is truly worrying. "It's a dark comedy." Pah. I tell him I reckon Natural Born Killers features more Hollywood headcases than any film made – Harrelson, Robert Downey Jr, Tom Sizemore, Tommy Lee Jones, Juliette Lewis. "I know, it was a mad little time. After we'd been working on it for a while, I felt I was the sanest guy in it. I really did. This has never happened… I'm the sanest guy in the whole deal." He whoops at the very idea. Who was the most insane? "Tom and Juliette went a little crazy. Yeah. I felt in a way Oliver encouraged madness. He needed to create that mayhem because that's what was on the screen."

He could, for instance, easily have ended up as a minister of the church. His mother is a religious prestbyterian and so was he through his childhood. Did he see it as a calling? "I did a little bit." He studied theology alongside drama at university, and it was only then that his belief system started to collapse. "I remember Dr Matthews; a great teacher teaching progressive ideas. I started seeing through the way the Bible got constructed. For example, there were two angels outside the tomb when Jesus rolled back the stone and rose from the dead. Why? Because in Jewish law there had to be two witnesses for it to be legal. But when it was first written it was one, so little things like that."

Talk to Harrelson and you might think his reverse Damascene conversion was the first significant event in his life. But it wasn't – by a long stretch. In the past, he's been surprisingly private about his family life. He would talk about the love for his mother, his two brothers, growing up in Texas and Ohio, and it seemed a pretty regular childhood. I've read that Harrelson's father was a contract killer but assume it's an urban myth – one of those apocryphal stories actors come up with when bored. I ask him how he got on with his father. "Pretty good," he says. "They separated young, he was not around too much." Then nothing. He ended up in prison? "Yeaah," he says slowly as if chewing on a tobacco leaf. "Yes. That explains his absence." He laughs wryly, and waits for the subject to change.

You're the first star I've interviewed whose dad was a professional killer, I say. No comment. I tell him I recently interviewed a woman whose son became a serial killer, and that she had been suicidal as a result. He looks interested. "Ah man, that must have been devastating for her. You never really think of that shit when you hear these stories," he says quietly. He tells me a bit more about his father. "I think they separated when I was seven. But he was gone a lot before that, in prison. Away and back. Away and back. It wasn't like he was there all the time prior to that."

"They call him a contract killer in the cuttings," I say. "Is that a glamorisation or simplification of what he did?" Harrelson chews some more on the imaginary tobacco. "Yeah, I mean that's probably a fair, erm…" He stops. Fair job summary? "Yeah, job summary. I was 11 or 12 when I heard his name mentioned on a car radio. I was in the car waiting for a lady who was picking me up from school, helping my mum, and anyway I was listening to the radio and it was talking about Charles V Harrelson and his trial for murder and blah blah blah blah and I'm sitting there thinking there can't be another Charles V Harrelson. I mean, that's my dad! It was a wild realisation. Then the woman got in the car and saw my face and realised something was up. She was a very kind lady."

He says he went home, in shock, and tried to talk to his mother about it. But there was little to say – the truth was out there, on the radio and in the papers. Did your mum know what he did for a living? "Oh yeah, she was pretty hip to all that." Did she love him? "Well, no, she was well out of love with him. You know, I've got to give her credit because she never really soured us on him, she didn't talk negative about him, never, ever. And she could have – he wasn't the greatest husband. Or father. But..."

Charles V Harrelson was jailed in 1973 for the murder of grain dealer Sam Degelia Jr. He was sentenced to 15 years, but released after five for good behaviour. In 1981 he was given two life sentences for the assassination of district judge John H Wood – the first murder of an American judge in the 20th century. At times, he also claimed to have assassinated John F Kennedy.

It was in 1981, after he heard his father had been arrested for killing the judge, that Woody tried to get in touch with him, aged 20. Were they ever reconciled? "Oh yeah, oh yeah. I tried for years to get him out. To get him a new trial." Why did you think he deserved a new trial? Harrelson stops, and thinks about it as if for the first time. "I don't know he did deserve a new trial… just being a son trying to help his dad. Then I spent a couple of million beating my head against the wall." A couple of million, I say, astonished. "Easily. Lawyers upon lawyers…"

Do you see much of your father in you? "Quite a bit… I was born on his birthday. They have a thing in Japan where they say if you're born on your father's birthday, you're not like your father, you are your father, and it's so weird when I would sit and talk with him. It was just mind-blowing to see all the things he did just like me." Such as? "Idiosyncratic things. The way he laughed. The face, very similar."

Did it scare you that you were so similar? "No, no." He laughs, uncertainly.

Charles V Harrelson died in prison in 2007. Were they friends by then? "Yeah, we got along pretty good. When you can't hang out and go to a pub, you know what I mean, it's hard."

It's difficult to imagine that Harrelson's character has not been shaped to some degree by his father – the early religion, the subsequent hell-raising, the campaigning (against environmental devastation, testing on monkeys, unethical energy, defence spending). He says if it were down to him, he'd scrap the defence budget and reallocate it. "The first thing I'd do is buy up every bit of rainforest or ancient forest – you could buy it all up with $2.5tn, no problem."

It's funny that you make such a convincing redneck, I say, when you are famous for your lefty-liberal views. He grins, and says it wasn't always like that. "I was a freshman in college in 1980, the year that Reagan was elected, and I went around badgering people to vote for him." What? Why? "I was part of the Young Republicans and bought all the bullshit. I'm embarrassed to tell you this because I really think he's one of the worst presidents in history. I was 18 when he went into office. Then almost immediately I noticed these cuts to the aid that I had to go to school – Reagan's first thing was to cut all the social shit."

By his early 20s, Harrelson had long given up on God and Reagan – he was starring in Cheers, had been introduced to environmental politics by fellow actor Ted Danson, and was having a wild time. He had a voracious appetite for pretty much everything. At one point, he was quoted as saying he slept with three women a day. Was that true? "No, no, no, no, not at all." He realises he might be protesting slightly too much, and starts again. "There was definitely a time of, what would you call it... of Satyricon. A time of definite excess, but I like to think everybody in that situation is probably going to go through that. I've always believed the road of excess leads to the palace of wisdom." He goof-grins. "It's been one of those thoughts that consoles me."

One of the many surprising things about Harrelson is that he has been with the same woman for 22 years. You wouldn't expect it, I say. "None of my friends did either. It is kind of shocking." Then he shocks me even more by telling the lovely, soppy story of how he and his wife got together. Laura was his assistant, and it was only over time he realised he was in love with her. "I went to Africa and I'm sitting around the fire out there, in Nairobi, thinking about her, fantasising about her." He looks embarrassed. "She's my assistant. It's baaaad! I came back from Africa and I couldn't even say I was in love with her because I was so nervous. I'd been sitting there with a guitar, so I wrote this song to her, and I sang it to her and at the end of it she goes, 'Woody, I've been in love with you for the last two and a half years.' Then I picked her up and carried her in." He and Laura finally married in 2008.

Harrelson takes out his phone to show me photos of Laura and his three daughters. "They are the best thing going. The oldest has just gone off to college. It was one of the single most difficult experiences of my life when it was time to separate and she walked off to the dorm and we drove away. I bawled my eyes out."

Twelve years ago the family moved to Hawaii. He'd been introduced to America's 50th state by the country singer Willie Nelson. "I went to see Willie play and at the end up comes Annie his wife and she goes, 'Willie wants to hang with you on the bus.' We open the door, and I see through the fog this guy holding up a big fatty. So I go in and start hanging with the Willie and I don't know this is going to become one of my best buddies in life." Nelson invited him to his home in Hawaii, Harrelson and Laura discovered Maui, the remote part of the island, and that was that. For three years he didn't make a movie – he just got on with remaking a life, hanging with the Willie on his porch, strumming guitar, smoking big fatties and writing (his play, Bullet For Adolf, co-written by Frankie Hyman, premiered in Toronto in 2003).

Are the hell-raising days over, then, or is he going to walk out of here and smack another photographer? "Oh yeah. I will never, ever even touch a cameraman. Never." It's funny how your sweet and scary sides happily coexist, I say. "Yeah. Heh! Heh! Heh! Heh!" And now he really does laugh like crazy. "Hey, man, the paparazzi, they will make you angry, that's their whole thing. It's a better picture. I've had a lot of expensive lessons on that score." With anger or the paparazzi? "The combination." Did something change in you? "No, I still have emotions bubble up, but I think I probably have a better rein on them. My whole thing now is I put my head down and keep walking."

A man comes into the room carrying two huge green smoothies.

"Hey, buddy!" Harrelson says.

"Hey, buddy!" the man says.

"This is Simon," Harrelson says. "This is Stan the man." He tastes the smoothie. "That is just awesome, the best smoothie on earth. Lots of berries, kale, kiwi, plum, pineapple, cinnamon, hemp seed." Harrelson eats mainly raw food. "There's a spoon right there, have some."

So I do, and it tastes wonderful.

"Wo, I can see you transforming in front of me," Harrelson says.

"It's good. Did you say that was kiwi in it?" I say.

"No," says Stan the man. "Ki-weed!"

"I forgot to tell you, it's spiked!" Harrelson says. And the pair of them fall about laughing.

As he finishes his smoothie, I say to Harrelson that he seems to have had a pretty amazing life. He nods and slurps. "It's quite a dichotomy," he says and he tells me one last story. "I was in a taxi the other night, and we started talking about life and the taxi driver goes, 'Chaos and creativity go together. If you lose one per cent of your chaos, you lose your creativity.' I said that's the most brilliant thing I've heard. I needed to hear that years ago."